Create an addon's own hidden window.

hidden-window.js

let Cc = Components.classes;
let Ci = Components.interfaces;
let appShellService = Cc['@mozilla.org/appshell/appShellService;1'].
                        getService(Ci.nsIAppShellService);
let ioService = Cc['@mozilla.org/network/io-service;1'].
                  getService(Ci.nsIIOService);


let uri = "data:application/xhtml+xml;charset=utf-8,<html/>"
let xulWindow = appShellService.createTopLevelWindow(
  null, // (Also tried no visible diff) appShellService.hiddenWindow
  ioService.newURI(uri, null, null),
  false,
  false,
  null,
  null,
  null,
  null);

appShellService.unregisterTopLevelWindow(xulWindow);

let domWindow = xulWindow.QueryInterface(Ci.nsIInterfaceRequestor).
    getInterface(Ci.nsIDOMWindow)